Encyclopedia of Algorithms

2008 Edition
| Editors: Ming-Yang Kao

Fast Minimal Triangulation

2005; Heggernes, Telle, Villanger
  • Yngve Villanger
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30162-4_142
How to cite

Keywords and Synonyms

Minimal fill problem        

Problem Definition

Minimal triangulation is the addition of an inclusion minimal set of edges to an arbitrary undirected graph, such that a chordal graph is obtained. A graph is chordal if every cycle of length at least 4 contains an edge between two nonconsecutive vertices of the cycle.

Open image in new window
This is a preview of subscription content, log in to check access.

Recommended Reading

  1. 1.
    Bouchitté, V., Todinca, I.: Treewidth and minimum fill-in: Grouping the minimal separators. SIAM J. Comput. 31, 212–232 (2001)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Bouchitté, V., Todinca, I.: Listing all potential maximal cliques of a graph. Theor. Comput. Sci. 276(1–2), 17–32 (2002)MATHCrossRefGoogle Scholar
  3. 3.
    Coppersmith, D., Winograd, S.: Matrix multiplication via arithmetic progressions. J. Symb. Comput. 9(3), 251–280 (1990)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Fomin, F.V., Kratsch, D., Todinca, I.: Exact (exponential) algorithms for treewidth and minimum fill-in. In: ICALP of LNCS, vol. 3142, pp. 568–580. Springer, Berlin (2004)Google Scholar
  5. 5.
    Heggernes, P., Telle, J.A., Villanger, Y.: Computing minimal triangulations in time \( { {O}(n^{\alpha}log\, n) = o(n^{2.376}) } \). SIAM J. Discret. Math. 19(4), 900–913 (2005)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Huson, D.H., Nettles, S., Warnow, T.: Obtaining highly accurate topology estimates of evolutionary trees from very short sequences. In: RECOMB, 1999, pp. 198–207Google Scholar
  7. 7.
    Kloks, T., Kratsch, D., Spinrad, J.: On treewidth and minimum fill-in of asteroidal triple-free graphs. Theor. Comput. Sci. 175, 309–335 (1997)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Kratsch, D., Spinrad, J.: Minimal fill in \( { {O}(n^{2.69}) } \) time. Discret. Math. 306(3), 366–371 (2006)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Parra, A., Scheffler, P.: Characterizations and algorithmic applications of chordal graph embeddings. Discret. Appl. Math. 79, 171–188 (1997)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Rose, D., Tarjan, R.E., Lueker, G.: Algorithmic aspects of vertex elimination on graphs. SIAM J. Comput. 5, 146–160 (1976)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Yngve Villanger
    • 1
  1. 1.Department of InformaticsUniversity of BergenBergenNorway